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    "# Lecture 25 - Variational Inference\n",
    "\n",
    "## Objectives\n",
    "\n",
    "+ to introduce variational inference as a class of techniques for approximate Bayesian Inference. \n",
    "+ to use automatic differentiation variational inference (ADVI) for performing Bayesian inference, using `PyMC3`.\n",
    "\n",
    "## References \n",
    "\n",
    "+ Variational Inference: A Review for Statisticians (Blei et al, 2018) - https://arxiv.org/pdf/1601.00670.pdf.\n",
    "\n",
    "+ Automatic Differentiation Variational Inference (Kucukelbir et al, 2016) - https://arxiv.org/pdf/1603.00788.pdf.\n",
    "\n",
    "+ Autoencoding Variational Bayes (Kingma and Welling, 2014) - https://arxiv.org/pdf/1312.6114.pdf\n",
    "\n",
    "+ Black Box Variational Inference (Ranganath et al, 2013) - https://arxiv.org/pdf/1401.0118.pdf.\n",
    "\n",
    "## Additional Reading \n",
    "\n",
    "+ Stein Variational Gradient Descent (Liu and Wang, 2016) (https://arxiv.org/pdf/1608.04471.pdf)\n",
    "\n",
    "+ Variational Inference with Normalizing Flows (Rezende and Mohamed, 2016) - https://arxiv.org/pdf/1505.05770.pdf.\n"
   ]
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    "import numpy as np\n",
    "import theano as th\n",
    "from theano import tensor as tt, shared\n",
    "import pymc3 as pm\n",
    "\n",
    "from scipy import stats as st \n",
    "from scipy import optimize \n",
    "\n",
    "\n",
    "import pandas as pd\n",
    "import arviz as az\n",
    "from graphviz import Digraph\n",
    "\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns \n",
    "sns.set()\n",
    "%matplotlib inline"
   ]
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    "## Bayesian Inference \n",
    "\n",
    "### Quick Review \n",
    "\n",
    "Once again, let's begin with a review of Bayesian inference. \n",
    "\n",
    "Our goal is to derive a probability distribution over unknown quantities (or latent variables), conditional on any observed data (i.e. a posterior distribution). \n",
    "Without loss of generality, we denote all unknown quantities in our model as $\\theta$ and the observed data as $\\mathcal{D}$. \n",
    "\n",
    "We start with a description of our prior state of knowledge over $\\theta$ - $p(\\theta)$. \n",
    "\n",
    "We then specify a conditional probabilistic model that links the observed data with the unknown quantities $p(\\mathcal{D}|\\theta)$ (the likelihood). \n",
    "We want $p(\\theta|\\mathcal{D})$ which we know, from Bayes rule, to be:\n",
    "$\n",
    "p(\\theta | \\mathcal{D}) \\propto p(\\mathcal{D}, \\theta).\n",
    "$\n",
    "\n",
    "The posterior distribution $p(\\theta | \\mathcal{D})$ captures our state of knowledge about $\\theta$ conditional on all the information available to us $\\mathcal{D}$. \n",
    "\n",
    "In the Bayesian framework, predictions about unseen data (or test data), are posed as expectations over this posterior distribution.\n",
    "\n",
    "\n",
    "### What is the problem? \n",
    "\n",
    "Unfortunately, as you already know, the posterior distribution is more often than not unavailable in closed form. \n",
    "This is due to the intractablity of the *evidence* (or *marginal likelihood*), i.e., the denominator in the Bayes' rule, $Z = \\int p(\\theta, \\mathcal{D}) \\mathrm{d}\\theta$.\n",
    "Infact, there are only a small class of prior-posterior models that admit closed form expressions for the posterior distributions (*conjugate models*). \n",
    "\n",
    "### Approximating the posterior\n",
    "\n",
    "There are several approaches to do this:\n",
    "\n",
    "1. The posterior density $p(\\theta | \\mathcal{D})$ is approximated with a point mass density, i.e., $p(\\theta | \\mathcal{D})  = \\delta_{\\theta^*}(\\theta)$, where, $\\delta_{\\theta^*}(\\theta) = \\begin{cases}  1, \\text{ if } \\theta = \\theta^*, \\\\  0 \\text{ otherwise.} \\end{cases}$\n",
    "This is the well-known *maximum a-posteriori* (MAP) estimation procedure. The parameter $\\theta^*$ is obtained as the solution of the optimization problem, $\\theta^* = \\underset{\\theta}{\\mathrm{argmax}} p(\\theta, \\mathcal{D})$. The MAP approximation is often justified by the assumption that the true posterior distribution $p(\\theta|\\mathcal{D})$ has a single, sharply peaked mode. In practice this approach often provides reasonable predictive accuracy but is unable to capture any of the epistemic uncertainty induced by limited data.\n",
    "\n",
    "2. The posterior distribution is approximated with a finite number of particles, i.e., $p(\\theta | \\mathcal{D}) = \\sum_{i=1}^{N} w^{(i)} \\delta (\\theta - \\theta^{(i)})$.  The most popular class of techniques that approximates the posterior distribution this way is Markov Chain Monte Carlo (MCMC). Recall that the general idea of MCMC is to construct a discrete-time, reversible and ergodic Markov Chain whose equilibrium distribution is the target posterior distribution. The goal is to simulate the Markov Chain long enough that it enters it's equilibrium phase (i.e. target posterior density). Once this is accomplished, sampling from the Markov Chain is the same as sampling from the target posterior density. Since MCMC samples (in theory) directly from the posterior, the weights of the approximation $, w^{(i)}$ are simply set to 1. \n",
    "There are several other approaches to approximate probability densities with particle distributions such as Sequential Monte Carlo (SMC) (which developed primarily as tools for inferring latent variables in state-space models but can be used for general purpose inference) and Stein Variational Gradient Descent (SVGD). \n",
    "\n",
    "3. Set up a parameterized family of densities over the latent variables - $q_{\\phi}(\\theta)$, and infer the parameters, $\\phi$ by solving an optimization problem of the form:\n",
    "$$\n",
    "\\phi^{*} = \\underset{\\phi}{\\mathrm{argmin}} \\ \\mathrm{D}[ p(\\theta| \\mathcal{D}) , q_{\\phi}(\\theta)], \n",
    "$$\n",
    "where, $\\mathrm{D}[\\cdot, \\cdot]$ is some measure of discrepancy between the approximate (or *variational*) posterior and the true posterior. \n",
    "Needless to say, we want to set up this optimization problem such that we only need to know $p(\\theta | \\mathcal{D})$ upto a multiplicative constant. \n",
    "*Variational Inference* (VI) is the name given to this general class of methods that seek to approximate the posterior this way. \n",
    "\n",
    "\n",
    "### Variational Inference \n",
    "\n",
    "Different VI procedures are obtained based on different choices of the approximating family $q_{\\phi}(\\cdot)$ and the functional $\\mathrm{D}[\\cdot, \\cdot]$. The most standard choice for $\\mathrm{D}$ is the *Kullback Leibler (KL) divergence*.\n",
    "The KL divergence between two densities $q(\\theta)$ and $p(\\theta)$ is defined as follows: \n",
    "$$\n",
    "\\mathrm{KL}[q(\\theta)|| p(\\theta)] = \\int q(\\theta) \\log \\left( \\frac{q(\\theta)}{p(\\theta)} \\right) \\mathrm{d}\\theta = \\mathbb{E}_{q(\\theta)} \\left[ \\log \\left( \\frac{q(\\theta)}{p(\\theta)} \\right) \\right].\n",
    "$$\n",
    "The KL divergence is always non-negative, i.e., $\\mathrm{KL}[q(\\theta)|| p(\\theta)] \\ge 0$, with $\\mathrm{KL}[q(\\theta)|| p(\\theta)] = 0$ implying that $q(\\theta) = p(\\theta)$ *almost everywhere*. \n",
    "Our inference goal can, therefore, be stated as follows - given a choice of a family of densities $q(\\cdot)$, parameterized by $\\phi$, what is the setting of $\\phi$ that will return the closest match, i.e. minimum KL divergence, between the approximate posterior $q(\\theta)$ and the true posterior $p(\\theta|\\mathcal{D})$?\n",
    "\n",
    "This brings us to $q$ - the approximate posterior. Notice that we have made no assumptions on $q$ thus far. We can, ofcourse, pick any arbitrary distribution we want to approximate the posterior. However, in practice, we pick $q$ such that it satisfies some desirable properties:\n",
    "1. If we know that a latent variable has finite support (positive reals for instance), we pick $q$ such $q$ itself has support on the same interval only. \n",
    "2. We would also like $q$ to be easy to sample from and easy to evaluate it's log probability since the variational objective requires computing an expectation over log probability ratios. A common simplfying assumption that enables easier sampling and log probability computation is the *mean-field* assumption - i.e., setting up approximation such that the individual latent variables are independent. If $\\theta = (\\theta_1, \\theta_2, \\dots, \\theta_M)$ is the vector of latent variables, the mean-field assumption implies an approximation of the form,\n",
    "$$\n",
    "p(\\theta|\\mathcal{D}) \\approx q_{\\phi}(\\theta) = \\prod_{i=1}^{M} {q_{i}}_{\\phi_i}(\\theta_i),\n",
    "$$\n",
    "where $q_{\\phi_i}(\\cdot)$ is the approximate marginal posterior over the latent variable $\\theta_i$ parameterized by $\\phi_i$.\n",
    "\n",
    "### Evidence Lower Bound (ELBO)\n",
    "\n",
    "So, to recap, the generic VI strategy is to pose a suitable parameterized family of densities $q_{\\phi}(\\theta)$ to approximate the true posterior $p(\\theta|\\mathcal{D})$ and to minimize the KL divergence from $q$ to $p$:\n",
    "$$\n",
    "\\phi^* = \\underset{\\phi}{\\mathrm{argmin}}\\ \\mathrm{KL}\\left[ q_{\\phi}(\\theta) || p(\\theta|\\mathcal{D}) \\right].\n",
    "$$\n",
    "We cannot actually optimize the KL divergence directly because of it's dependence on the true posterior $p(\\theta | \\mathcal{D})$.\n",
    "Instead, we will solve an equivalent, tractable optimization problem. Define the function $\\mathcal{L}(\\phi)$ as $\\mathcal{L}(\\phi) =  \\mathbb{E}_{q(\\theta)}[\\log p(\\theta, \\mathcal{D})] + \\mathbb{H}[q(\\theta)]$, where, $\\mathbb{H}[q(\\theta)] =\\mathbb{E}_{q(\\theta)}[-\\log q(\\theta)] $  is the *entropy* of $q$. With some simple algebra you can show that solving the optimization problem:\n",
    "$$\n",
    "\\phi^* = \\underset{\\phi}{\\mathrm{argmax}}\\ \\mathcal{L}(\\phi), \n",
    "$$\n",
    "is equivalent to minimizing the KL divergence between $q$ and $p(\\theta|\\mathcal{D})$.\n",
    "\n",
    "**Proof**:\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathrm{KL}\\left[ q_{\\phi}(\\theta) || p(\\theta|\\mathcal{D})  \\right] &= \\mathbb{E}_q \\left[  \\log \\left( \\frac{q_{\\phi}(\\theta)}{p(\\theta|\\mathcal{D})} \\right) \\right], \\\\\n",
    "&= \\mathbb{E}_q \\left[ \\log \\left( \\frac{q_{\\phi}(\\theta) Z}{p(\\theta, \\mathcal{D})} \\right) \\right], \\ \\text{where $Z$ is the evidence,} \\\\ \n",
    "&= \\underset{=-\\mathbb{H}[q(\\theta)]}{\\underbrace{\\mathbb{E}_q [\\log q_{\\phi}(\\theta)]}} - \\mathbb{E}_q [\\log p(\\theta, \\mathcal{D})] + \\underset{\\text{this is a constant}}{\\underbrace{\\log Z}},\\\\\n",
    "&= - \\mathcal{L}(\\phi) + \\log Z.\n",
    "\\end{align}\n",
    "$$\n",
    "Therefore, \n",
    "$$\n",
    "\\log Z = \\mathrm{KL}\\left[ q_{\\phi}(\\theta) || p(\\theta|\\mathcal{D})  \\right] + \\mathcal{L}(\\phi).\n",
    "$$\n",
    "\n",
    "Now we see that the log evidence (which is a constant) is the sum of the objective function $\\mathcal{L}(\\phi)$ and the KL divergence between the true and approximate posteriors.\n",
    "Since, the KL divergence is non-negative, the objective $\\mathcal{L}(\\phi)$ is a lower-bound on the log evidence. The bound is tight, i.e., $\\log Z = \\mathcal{L}(\\phi)$, if $q_{\\phi}$ matches the true posterior perfectly. Minimizing the KL divergence wrt to the variational parameters, $\\phi$ is equivalent to maximizing the objective $\\mathcal{L}(\\phi)$ wrt to $\\phi$ and since  $\\mathcal{L}(\\phi)$ depends on terms that we know and can compute and/or approximate, we use it as the objective function for our VI optimization problem. $\\mathcal{L}(\\phi)$ is also known as the Evidence Lower Bound or ELBO.\n",
    "\n",
    "One of the nice things about the ELBO is that it has a neat interpretation. The ELBO is a sum of two terms:\n",
    "1. $\\mathbb{E}_{q(\\theta)}[\\log p(\\theta, \\mathcal{D})]$ is a measure of the expected model fit under the approximate posterior density. \n",
    "2. $\\mathbb{H}[q(\\theta)]$ - the entropy of the approximate posterior acts a regularizer. The entropy of a distribution is a measure of how \"diffuse\" it is. In maximizing the entropy, we try to construct our posterior approximation such that it accounts for the maximum ammount of uncertainty in the latent variables conditional on the observed data. \n",
    "\n",
    "The two terms in the objective function $\\mathcal{L}(\\phi)$ therefore have an associated trade-off - in optimizing the ELBO we are simultaneously trying to achieve the best possible fit to the data without introducing any excess bias that is not supported by the data (see [the principle of maximum entropy](https://en.wikipedia.org/wiki/Principle_of_maximum_entropy) for assigning probability distributions).\n",
    "\n",
    "Another nice by-product of doing Bayesian inference by maximizing the ELBO is that we can perform Bayesian model selection. Bayesian model selection relies on the estimation and comparison of the model evidence $Z$ (or it's log) and in VI we work with an approximation to this quantity."
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    "### Automatic Differentiation Variational Inference (ADVI)\n",
    "\n",
    "Suppose you have put together the joint probability model $p(\\theta, \\mathcal{D})$. The latent variables that have to be inferred are $\\theta = (\\theta_1, \\theta_2, \\dots, \\theta_M)$. Variational inference in generic probability models can become extremely tedious and complicated due to the fact the individual $\\theta_i$s may come from different probability spaces and have different supports. This means that the user must pose appropriate variational distributions for each $\\theta_i$ and derive gradients of the probability model, $p$, wrt to the individual latent variables separately. Furthermore, taking the gradient of the ELBO wrt to the variational parameters require differentiating through a sampling procedure for approximating the datafit term - $\\mathbb{E}_{q(\\theta)}[\\log p(\\theta, \\mathcal{D})] \\approx \\frac{1}{S} \\sum_{s=1}^{S}\\log p(\\theta^{(s)}, \\mathcal{D}), \\theta^{(s)} \\sim q(\\theta)$. \n",
    "It turns out that the estimator of ELBO gradient obtained this way has very high variance. \n",
    "This high variance problem is alleviated by means of the *reparameterization trick* (see Kingma's paper on Autoencoding Variational Bayes). \n",
    "\n",
    "\n",
    "To the greatest extent possible, we would like to automate the variational inference procedure and for this we will explore the ADVI approach to variational inference. ADVI requires the user to specify two things only - \n",
    "1. the joint probability model $p(\\theta, \\mathcal{D})$, and,\n",
    "2. the dataset $\\mathcal{D}$. \n",
    "\n",
    "**How does ADVI work?**\n",
    "\n",
    "1. First, ADVI transforms all latent variables, i.e. all $\\theta_i$s into new variables $\\zeta_i$s by means of a suitable invertible transformation, i.e.,  $\\zeta_i = \\mathcal{T}(\\theta_i)$ such that $\\zeta_i$ will have support on the entire real space (recall from our discussion on MCMC with `PyMC3` that this transformation happened by default when specifying  `PyMC3` probability models). \n",
    "\n",
    "2. Now that all latent variables have same support, ADVI proceeds to specify a common family of distributions on all latent variables. The usual choice is to specify a multivariate Gaussian approximation:\n",
    "$$\n",
    "q_{\\phi}(\\theta) = \\mathrm{MVN}(\\theta| \\mu , \\Sigma),\n",
    "$$\n",
    "where, $\\phi = \\{ \\mu, \\Sigma \\}$ denotes the variational parameters. \n",
    "\n",
    "3. The approximate posterior is further reparameterized in terms of a standard Gaussian to remove the dependence of the sampling procedure from $\\phi$.\n",
    "\n",
    "4. Use standard stochastic optimization techniques to obtain estimates of the variational parameters.\n"
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    "## Example 1 - normal-normal model\n",
    "\n",
    "Let's demonstrate the VI process end-to-end with a simple example.\n",
    "\n",
    "Consider the task of inferring the gravitational constant from data (seen previously in Lec. 6). \n",
    "\n",
    "We perform an experiment $X_n$ that measures the acceleration of gravity and that we know that the measurement variance is $\\sigma = 0.1$."
   ]
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     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.constants\n",
    "g_true = scipy.constants.g\n",
    "# Generate some synthetic data\n",
    "N = 10\n",
    "sigma = 0.2\n",
    "data = g_true + sigma * np.random.randn(N)\n",
    "plt.plot(np.arange(N), data, 'o', label='Data')\n",
    "plt.plot(np.linspace(0, N, 100), g_true*np.ones(100), '--', label='True value')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we have:\n",
    "$$\n",
    "X_n | g, \\sigma \\sim N(g, \\sigma^2).\n",
    "$$\n",
    "So, the model says that the measured acceleration of gravity is around the true one with some Gaussian noise.\n",
    "\n",
    "Assume that our prior state-of-knowledge over $g$ is:\n",
    "$$\n",
    "g | g_0, s_0 \\sim N(g_0, s_0^2),\n",
    "$$\n",
    "with known $g_0 = 10$, $s_0 = 0.4$.\n",
    "\n",
    "This is a conjugate model and the posterior over $g$ is given by:\n",
    "$$\n",
    "g|X \\sim N(\\tilde{g}, \\tilde{s}^2),\n",
    "$$\n",
    "where, $\\tilde{s}^2 = \\left( \\frac{N}{\\sigma^2} + \\frac{1}{s_0^2} \\right)^{-1}$ and $\\tilde{g} = \\tilde{s}^2 \\left( \\frac{g_0}{s_0^2} + \\frac{\\sum_{i=1}^{N} X_i}{\\sigma^2}\\right)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def post_mean_and_variance(prior_mean, prior_variance, data, likelihood_var):\n",
    "    N = len(data)\n",
    "    sigma2 = likelihood_var\n",
    "    s02 = prior_variance\n",
    "    m0 = prior_mean\n",
    "    sumdata = np.sum(data)\n",
    "    post_prec = (N/sigma2) + (1./s02)\n",
    "    post_var = 1./post_prec\n",
    "    post_mean = post_var * ((m0/s02) + (sumdata/sigma2))\n",
    "    return post_mean, post_var\n",
    "\n",
    "gtilde, s2tilde = post_mean_and_variance(10., 0.4**2, data, 0.1**2)\n",
    "\n",
    "xs1 = np.linspace(7, 12, 100)\n",
    "xs2 = np.linspace(8, 11, 100)\n",
    "plt.plot(xs1, st.norm(loc=10., scale=0.4).pdf(xs1), label='Prior')\n",
    "plt.plot(xs2, st.norm(loc=gtilde, scale=np.sqrt(s2tilde)).pdf(xs2), label='Posterior')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try to infer the posterior over $g$ using VI. Let specify our joint log probability model first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from autograd.scipy.stats.norm import logpdf as normlogpdf\n",
    "from autograd import grad, elementwise_grad as egrad \n",
    "from autograd import numpy as anp\n",
    "from autograd.numpy import random as npr\n",
    "from autograd.misc.optimizers import adam \n",
    "\n",
    "g0, s0 = 10., 0.4\n",
    "sigma = 0.1\n",
    "\n",
    "def logprior(g):\n",
    "    return normlogpdf(g, g0, s0)\n",
    "\n",
    "def loglikelihood(g):\n",
    "    return anp.sum(normlogpdf(data, g, sigma))\n",
    "\n",
    "def logjoint(g):\n",
    "    return logprior(g) + loglikelihood(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to specify a parameterized approximate posterior, $q_{\\phi}(\\cdot)$. The obvious choice here is a Gaussian:\n",
    "$$\n",
    "q_{\\phi}(g) = N(g | \\phi_1, \\exp(\\phi_2)^2),\n",
    "$$\n",
    "where, $\\phi = (\\phi_1, \\phi_2)$ are the variational parameters. The ELBO needs to be maximized wrt to $\\phi$. Let go ahead and set up the ELBO. Recall that the ELBO is given by:\n",
    "$$\n",
    "\\mathcal{L}(\\phi) =  \\mathbb{E}_{q(\\theta)}[\\log p(\\theta, \\mathcal{D})] + \\mathbb{H}[q(\\theta)].\n",
    "$$\n",
    "\n",
    "To optimize the ELBO, we will need to compute an expectation over the variational distribution $q$ (first term on the RHS in the above equation). This cannot be done analytically. Instead, we resort to a Monte Carlo approximation:\n",
    "\n",
    "$$\n",
    "\\mathbb{E}_q [\\log p(\\theta, \\mathbf{x})] \\approx \\frac{1}{S}\\sum_{s=1}^{S}   \\log p(\\theta^{(s)}, \\mathbf{x}),\n",
    "$$\n",
    "where the samples $\\theta^{(s)}$ are drawn from $q$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def norm_entropy(s):\n",
    "    s2 = s*s\n",
    "    return 0.5 * (1. + anp.log(2.*anp.pi*s2))\n",
    "\n",
    "def ELBO(phi, num_samples):\n",
    "    m, s = phi[0], anp.exp(phi[1])\n",
    "    \n",
    "    # compute the entropy \n",
    "    entropy = norm_entropy(s)\n",
    "    \n",
    "    # compute the avg. datafit\n",
    "    samples = m + s*npr.randn(num_samples)\n",
    "    datafit = 0.\n",
    "    for sample in samples:\n",
    "        datafit += logjoint(sample)\n",
    "    datafit = datafit/num_samples\n",
    "    \n",
    "    # return the elbo\n",
    "    elbo = datafit + entropy\n",
    "    return elbo\n",
    "\n",
    "def negELBO(phi, num_samples=5):\n",
    "    return -ELBO(phi, num_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's optimize the lower bound using simple stochastic gradient descent (SGD)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration [  50] : ELBO = -9.21201\n",
      "Iteration [ 100] : ELBO = -4.84956\n",
      "Iteration [ 150] : ELBO = -4.09946\n",
      "Iteration [ 200] : ELBO = -5.56783\n",
      "Iteration [ 250] : ELBO = -4.04894\n",
      "Iteration [ 300] : ELBO = -3.92402\n",
      "Iteration [ 350] : ELBO = -3.97946\n",
      "Iteration [ 400] : ELBO = -5.41017\n",
      "Iteration [ 450] : ELBO = -3.71515\n",
      "Iteration [ 500] : ELBO = -4.18543\n",
      "Iteration [ 550] : ELBO = -4.49978\n",
      "Iteration [ 600] : ELBO = -3.88569\n",
      "Iteration [ 650] : ELBO = -3.79997\n",
      "Iteration [ 700] : ELBO = -4.83628\n",
      "Iteration [ 750] : ELBO = -4.34290\n",
      "Iteration [ 800] : ELBO = -4.38020\n",
      "Iteration [ 850] : ELBO = -3.61004\n",
      "Iteration [ 900] : ELBO = -4.05194\n",
      "Iteration [ 950] : ELBO = -3.96508\n",
      "Iteration [1000] : ELBO = -4.10269\n"
     ]
    }
   ],
   "source": [
    "# get the gradient of the negative elbo \n",
    "gradnegelbo = grad(negELBO)\n",
    "\n",
    "# give initial values to the variational parameters \n",
    "phi_init = anp.array([9., -1.])\n",
    "\n",
    "# optimize \n",
    "num_iter = 1000\n",
    "phi_i = phi_init\n",
    "step_size = 1e-3\n",
    "num_samples = 10\n",
    "elbos = []\n",
    "bestnegelbo = np.inf\n",
    "for i in range(num_iter):\n",
    "    negelbo = negELBO(phi_i, num_samples)\n",
    "    elbos.append(-negelbo)\n",
    "    grad_i = gradnegelbo(phi_i, num_samples)\n",
    "    phi_next = phi_i - step_size*grad_i\n",
    "    \n",
    "    if (i+1)%50 == 0:\n",
    "        print('Iteration [%4d] : ELBO = %.5f'%(i+1, -negelbo))\n",
    "        if negelbo < bestnegelbo:\n",
    "            phi_opt = phi_i\n",
    "            bestnegelbo = negelbo   \n",
    "    phi_i = phi_next"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.plot(np.arange(num_iter), elbos)\n",
    "plt.title('ELBO vs SGD Iterations');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the posterior distribution\n",
    "postmean = phi_opt[0]\n",
    "poststdev = np.exp(phi_opt[1])\n",
    "gpost = st.norm(postmean, poststdev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cxrZtW1my5Bncbg/f/vZ3x3xV4HC+9a3/zTXXXMVNN93Is88+zezZB/Dee+tYsWI5LS2t/K//Zfd28nq9XHnlF/jpT2/is5+9kPnzT6GqqorXX3+F1atXceaZZzF9+kwAWlvtK3ueeeZJamqqWbBgEfvtN5vrrvsu//Zv3+Hyyy9m/vxTaGlp4bXX7NcffPAhfPrTnx31+F0uF9/5zv/hG9/4Ctdd9410H6mprFz5Jm+//RYzZ87immu+WrDzJbI3yW190Na86xqpCY3VeNwukilTW8VIWRjL0t6VwETg2kAgkGnl/KdgMHjDMK+RMnDCCSdyww3/l/vvv5vHHnuEhoZGFi5cxAUXXMQ55ywY8tzGxkZuvfVO7r57MUuWPMNDD/2WhoZGTjjhRC655MohV5wV0rRp07n99rtZvPh2li59gTfeeI2WllbOP/8iLrnk8iEd1c8//yIaG5t46KHf8vTTTzAwEGXatOl85Stf57zzLsw+r61tEldd9UUefPABfv/73zFjxiz22282p556OhMmTOCeexazbNlLRKNRJk2axKWXXsmnP/1Po25imjFnzhHpz3AbL7/8d5YvX8rEiW1ccskVXHzxJWM+rsjeriOnq/mEphrCfQM7PcftcjG5pYYNW8O6ck/KgmGV/tK2mcD7I6mRam9fT1vbjDG9yd5aI1XOdM5Lp719PXPmHKaahhJSDUnxLf7Lap5/cwv+Gi/3f/+s3Z7vOx5ZxYsr26mt9nLzP8/bqY5TRk8/37uXUyM1C/hgp8dLPSAREZFdySzttezQ0XxHmc2LwwMJ+iIl7QUtshMFKRERKQuZHlKtDcP3bJs6YbB+apOW98RhClIiIuK4ZMqkuy8GQGvD8DNS03L23NuoK/fEYQpSIiLiuO5QDDNds9tSv/OMVKprI7HX/owVH6DOV0Fttd1ParOu3BOHKUiJiIjjcntI7TgjZZkmA4//lPiK3xN98R67MW+6n5SW9sRpClIiIuK4zpzWBy07BKnUlnewwvYm9cn3/o4VDTOl1a6T2twZIWXqamFxjoKUiIg4LnPFnmFAk3/oJt7Jd5cNfpFKklj7ElPTdVLJlMm27Tv3mxIpFQUpERFxXCZINddV4XEP/mqyUgkS77085LmJd55jWuvglXsqOBcnKUiJiIjjMkt7OxaaJze+BfF+AFytswAwt2+mzWwn04ZTdVLiJAUpERFxXLYZ5w71Ucl16WU9TyXVp30RDLf99brnaW20n6sr98RJClIiIuKoaDxJqD8BQGvOjJQVHyC5/nUAPDPn4qqbgGfGkQAk3/07UxrsX2GZ/lMiTlCQEhERR+VesZfb+iC5/jVI2VvAePf/qP3/g0+yH0zFmcO7APRGFKTEOQpSIiLiqI6cHlK5S3uJ9LKeUVmLe+phALinHIZR2wzAAdE3AIu+SCLbzFOk1BSkytg3vvFl5s07hueff3bY56VSKc4++ww+/vETGRiw/0L68pc/z7x5x7Bly4fDvnbLlg+ZN++Ynf478cSPcPrp8/inf7qAW265mb6+3kJ9rGH9/e/LWL367YIf9447fs28ecewZMmzBT+2iOSnsydnRiq9tJfq7yO1yf67wLPfRzBcHgAMlwtvYD4AdbGtTHN3YVoW4YFEiUctYvM4PQDZvQULFvH3vy/jqaee5MQTT97t81asWM727d0sXLiI6urh96janba2SSxcuGjIff39/bz66gruv/8eXnzxeW677W5qamrGdPyRePjhh/jxj2/kBz+4iYMPLuyxjzrqaABmzJhZ2AOLSN46eu1/AFZ4XNT5KgCIrF4KVgoAz/4fG/J8b+BE4q/+ASyL4yrXsrG/hb5wnLqaitIOXAQFqbJ20kknU1Pj48UXlxCNRqmq2vWO6E8++RjATkFoNNraJnHFFV/Y6X7TNPnWt77G8uUv8bvf3c+ll1455vfYk+7urqIde+7cY5g795iiHV9Exi4zI9XSUI1h2E0Nwm8/D4Dha8LddsCQ57tqm3BPO5zUhjc4uvJ9/tB/DL2ROFNLO2wRQEt7Za2ysopTTjmNgYEBXnrphV0+JxqNsmTJc0yaNDk761JILpeLiy66GIBly14q+PFFRDIzUpkeUma4i+jG1QB4Zh+LYez8q6rioJMBqDKSzK34gJ6wCs7FGZqRKnMLFy7i0Uf/xFNPPc6pp56+0+MvvPAcAwP9XHTRxdl/yRVaa+sEAHp7e4bcv3r129x99294443XiUYHmDx5CmecsZCLLvonKioGp9j7+/u5/fZfsmzZS7S3b6Gmxsfhhx/JJZdcQSBwEGDXdL3++qsA/O///c30ZxvsZvz003/jd7+7n3ffXYthuDj44EO45JIrhswyvfrqy/zzP1/Ntddez+uvv8rzzz+H31/L97//Q1asWM7ixbfxgx/cxPz5J2dfs2LFMu67725WrXqbZDLJzJkzWbToXM499zxcrsG/vOfNO4aFCxcxbdp07r//bgAuu+wqLrzw4kKcYpF9lmVZ2RmpzBV7yXeXZx/37n/cLl/nnn44VDfAQA9HVqynKxIv/mBFdkEzUmXuiCOOYtKkKSxd+hL9/Tt3733iib9iGAYLFnyiaGPYtGkjMBioAJYseZarr76c5cuX8pGPHMs555yH2+3m1ltv4etfv4Z4fPAvtRtuuJ7f/e4Bpk6dzgUXfJrjjjuBZcte4pprrmTDhg8AOOussznyyLkAnHbax7nssquyr7/99l9xww3X09XVycKFi1i48BO8//57fO1rX+Lxx/+y03gXL76Nd95Zxfnnf4oDDzyIAw88aJef66GHfsvXv/5l3nlnFfPnn8wnPvEPhMNhfvKTH/Jv//YdrB2uAlq+fCn33XcXCxYs4thjj+PQQ+eM7YSKSFZoIEEsYddCZQrNM1fruRom4WqevsvXGS43nkkHAjDB3UevgpQ4RDNSZc4OSWexePFtvPDCEs44Y2H2sd7eHv7+96UcccRRTJlSnOqAWCzG3Xf/BoCTTjoFgEgkzH/8x/eoqqriZz/7dXZWCUy+971/5YknHuP+++/m0kuv5L331rFs2UssWPAJ/uVf/i173OOPn8d3v3s9f/7zH7nmmq9y1llns2XLh7z++qucdtqZ2VmjVatWctddd3DUUUfzn/95c7ZO7PLLP88XvnAZ//mfP+DYY4+jsbExe+z+/giLF99Hc3PLbj/X5s2b+O///i8mTmzjZz/7Vfb8DQwMcP313+Cpp57kuOPmDQmo3d1d3HjjT5g3b37e51VEbDu2PrDiA5hdGwDwzDpm2Jl2V/1EABpdEULh/uIOVGQ3xm2QSm17j9irf4REdJePG4ax04xCyXmrqJx7Du4J++V1mAULPsHixbfxt789MSRIPf3030gmk3kVmWe0t2/hjjt+PeS+7du7s8txc+YcwTnnnAfA888/RyjUx6WXXpkTosDj8fCVr3yD5557mkce+SOXXnolpml/Dz744H36+nqpq6sH4MQTT+Z3v/sjEye2DTuuRx/9E5Zlcc01Xx1SbF9f38DFF1/CD3/4f3n66Sc577xPZR87/PAjhw1RAE8++VdSqRSXXXbVkBBaXV3NV7/6TT73uQt55JE/DglSlZWVHHfcCcMeV0RGZ0jrg4ZqzL5t2a9dTdOGfa2rzp4ldxkWVqizOAMU2YNxG6Tibz1BasMbTg9jj+IV1VSfenVex5gyZSpz5hzBihXLCIVC+P1+wA4DVVV2QXq+2tu3sHjxbdmvXS4XNTU1TJs2g3PPPY8LLrgIj8f+cVm7dg1gLzvuqLGxkenTZ7B27RrC4TCzZ+/PYYcdzsqVb/LJT57FUUcdzcc+djwnnDCfyZOn7HFcweA7ADz77NO8+OLzQx7r6LD/wl23bs2Q+9vaJu3xuGvXBgGyy4m59ttvNrW1ftatWzvk/gkTJuJ2u/d4bBEZuc7enBmp+irMzTlBqq512NcadYPlBu5+BSlxxrgNUhVzzsBKDJT9jFTFYWcU5FALFy7irbfe4LnnnmbRonNob9/CW2+9wRlnLKSmxpf38Y88ci4///mtI3puplartrZ2l4+3tLSydu0aotEotbW1/OQnP+f+++/m8ccfY9myl1i27CV++tObOOaYY7nuun9h0qTJu32vcDgEwL333rnb5+zYLLSyctdtInJFIvZn8Pl2/xk2b9446uOKyOhklvZqq71UV3qIhzqyj7lygtKuZJb2AKrj3cUZoMgejNsg5Z6wHzULvr7bxz0eF8mkWcIRFdepp36cn/70Jp5++kkWLTqHJ598HMuyOOuss0s+lkxTzs7Ojl0+HgrZ4aeuri77/CuvvJorr7yaDRvWs2LFMp544q+8/PLfueGGb3PbbXft9r2qq6txu9089dSL2RmxwnwGX/Yz5NZXDX6GvuwypIgUT0emh1Sm9UF6ac9V5cOoHP4fiUZ1PSnDi9tKUGf2kkim8Ho0ayylpav2xona2lpOPHE+r7yyglAoxDPP/I2JE9scaTK5//72lTJvvPH6To9FImHWrg0ydeo0KioqWLt2Db/4xc2sXPkWANOnz+C88y7klltuZ+rU6axe/TaJhL21w66KSmfPPoBUKsWaNe/s9NjKlW/yy1/+N2+88dqoP8MBB9if4c03d37tpk0b6erqZNas/GrbRGTPMkt7mdYHZp/9DzRPw/D1k2D/nRGvtvfda3GFdOWeOEJBahxZsGARqVSKP/7x96xZ8w4LFnyiaL2jhjN//snU1tby8MMPZmuYAJLJJDff/GNisVi2SDuRiPPAA/dw1123D1lqjUQihMN9NDc34/V6AbIzTplgBWRn3P77v39CJBLO3t/fH+Gmm27kvvvuIpVKjfoznHHGQtxuN3ffvZgPP9ycvX9gYICf/OSHAEVtKSEikDJNunrtRpotDUNnpLyNE3f7uiHH8NkXlrS4FaTEGeN2aW9fdOyxH6O5uYU777wdyG9LmHz4fLV8+9s3cMMN3+aLX7ycE088maamZl59dQXvvruOI444iosvvgSAQw45jJNPPpVnn32ayy+/mLlzP0IqlWTJkmfp6enh+uu/mz1upk/V3Xffwdq1QS677Crmzj2G88+/iIce+i2f/eyFHHfcCXi9FSxZ8gzbtm3l3HPPG9Os3JQpU/nyl7/OzTffxOWXX8yJJ55MdXU1y5a9xIcfbua0085QkBIpsu2hGGb6H1it9dVYZgorbG8V5W2cyEj+ieSqmwgdK2l2hfkgFAW0JC+lpSA1jrjdbs44YyEPPHAPhx9+JFOnDn9pcDGddNKp3HLLHdx11x0sX76URCLO1KnT+NKXvsqnPvXpIfVM3/3u9wgEDuHJJx/jT396GMMwCAQO4hvfuG5IT6ZTT/04S5e+yEsvPc/DDz/IWWctYvr0mXzta9/k4IMP4eGHH+Lxx/+C2+1m+vQZXHHFF/IKkxdccBHTpk3ngQfu4bnnnsGyTGbOnMVnP3sZixadk9f5EZE964sMzj431FbaIcqya1s9DW0jClIVjfYSoMcwGdjeAYxsJkukUAwHrmybCbzf1RXO9hjanfb29bS1zRjTm+xtxebjgc556bS3r2fOnMPo6Ag5PZR9RmurX+e7wF5f28nPfv8mAN/53NHMMDcy8JebAJh08f8h7Ju5x2PENq4k/pj9mtemf5b5C/JvB7Mv0s/37rlcBs3NtQCzgA92erzUAxIREQHo6x+saaqvqcgWmgN4Rlgj5c0tSg9v2/0TRYpEQUpERBwRyglS/pqKwa7mLjcef/OIjmH4mkimf5V51ZRTHKAgJSIijsjUSFV63VRWuLHSzTgNfwuGa2T9oAyXi5DLLjCvim8vzkBFhqEgJSIijsjMSPlr7BYo2Wace+hovqN+r91U159SkJLSU5ASERFHZGqk6nwVWJaVrZFy+YffY29HiSq7l1QjfZimLniR0lKQEhERR2SW9upqKrBiYUjYXc5HOyOVqrWDV4WRYqCnq7CDFNkDBSkREXFE7tKe1Td4xZ1RN7oZKU/9YPAKb9s8zDNFCq/sg5QDfa5Eypr+TMjewLQsQv3pGSnf0NYHo52RqmwcbIEQ7WovzABFRqisg5TL5R7TPmoie7NUKoVrhFc0iZSr/mgyuz3MkNYHgMs/uiBV09pGyji0f/8AACAASURBVLL3HU31bi3cIEVGYERbxAQCgTrgJWBRMBj8IBAInA78BKgG/icYDP5LMQZXWVlNNBqhtlZ7J4lkRKMRKiurnR6GSF76cjYYrqvxYnakWx9U12F4K0d1rHp/DR2mjxZ3GCPcsecXiBTQHmekAoHAR4EXgAPTX1cDvwHOAQ4GPhIIBBYWY3A+Xx39/SHC4V6SyaSWNGSfZVkWyWSScLiX/v4QPl+d00MSycuQIOWrwArZM1LGKJf1AHxVHrpMPwDeATXllNIayYzUVcA1wD3pr48F1gaDwfcBAoHAvcAFwGMFH5zHS1PTRCKRPrq72zHNkS/zuVwuXQZbYjrnxeVyuamsrKapaSIej9fp4YjkJXd7mLqc7WFG2/oAwDAM+twNwBaq49uxLAvDMAo1VJFh7TFIBYPBKwECgUDmrsnAlpynbAGmFnxkaR6Pl/r6kW0VkEsbMJaezrmIjFSm0BzAX2VgRexmmqMtNM/o9zZBCiqsGFYsjFHlL8g4RfZkRDVSO3ABuWtsBjDqaYj0TspF1dqqP0ilpnNeWjrfpaXzXTjJ9P8NA6b6E3yY/rVSP3U6/vR5HtX5rpsA6cbm9a4wVa2TCzjafYN+vsdmLEFqEzAp5+s24MPRHqSrK4xpFq/mSbMjpadzXlo636Wl811YWzvCAPiqvGzf+EH2/jB1RDtCoz7f8cqm7O3u9e/jrZg0zLNlR/r53j2Xyxh28mcsQWo5EAgEAvsD7wOfwS4+FxERGZG+3faQGn2NFKSbcqZbSCV7tqIqQimVUfeRCgaDUeBS4PfAKuAd4KHCDktERPZm2X32aryDPaQ8FRjVY2t34/f72J6qASC+XU05pXRGPCMVDAZn5tx+CjiiGAMSEZG9XyiS2R5msBmnyz9hzFfb1fkq6TT9NLr7SfVu2/MLRAqkrDubi4jI3im7tFdTgRVKtz4Y47IeQENtBZ0pu1jaFVaQktJRkBIRkZJKJE0GYvZ1e/4aT7ZGaizNODPqfRV0pptyuhMRrPhA/gMVGQEFKRERKalQTjPO5ooYpOzZqXxmpOp8gzNSwJC9+0SKSUFKRERKKrereSN92duj3aw4V4XXTcjTmP3a7NPmxVIaClIiIlJSfZHBruZ1Zm/29li7mmckqgd3wTBVcC4loiAlIiIllbu0V5NItyPHwPCPfjuwXNW+WkJmFQCWlvakRBSkRESkpHKX9iqi3QAYtU0Y7vzaaNbnXLmnpT0pFQUpEREpqVB6ac/jdmFEOoH8l/UA6tO9pADMUGfexxMZCQUpEREpqWxXc583uwTn8o/9ir2M+toKes1qAKz+HizLzPuYInuiICUiIiWVCVJN1WBF7Y1y8+khlVHvq6DXtLeJwUxhRcN5H1NkTxSkRESkpDJLe5Oqotn7XP6WvI87JEhhz0qJFJuClIiIlFRmRqrVG8veZ/gad/f0EavzVdBrVWe/tiIKUlJ8ClIiIlIylmVl2x80ege3cXHVNOR97PraSvpyZqTM/u3DPFukMBSkRESkZAZiKZIpC4A6YzBIGQUIUv5qLyFLS3tSWgpSIiJSMrk9pGqJ2DcqqjG8lXkf2+UyqPFVETbtY2lpT0pBQUpEREqmLzIYpKpNO0gVYlkvo95XQV9OCwSRYlOQEhGRksndHqYikW59UNAgVZm9cs9UkJISUJASEZGS6esf3LDYE+8DChuk6nze7JV7VkTF5lJ8ClIiIlIyoezSnoUx0AuAqwCtDzL8NYO9pKyBXixT3c2luBSkRESkZDLF5i2VKTCTABg19QU7vr/Gm62RwrKwon0FO7bIrihIiYhIyWSW9tp8g0t8Rk0BZ6Sqd+huriv3pMgUpEREpGQyS3sTK3O7mheuRqq2xrvDNjGqk5LiUpASEZGSySztNedsD1PI9gf+Gi+95uA2MaZmpKTIFKRERKRkQumlvUbP4IbFhbxqz19TQciqxrSbp6uXlBSdgpSIiJREyjQJD9hBym/023dW1GB4Kgr2Hv5qLyYuwlYVoKU9KT4FKRERKYlQTg+pWivd1byA9VEAVRVuPG5jsCmnlvakyBSkRESkJHK3h6lKhYHCXrEHYBgG/hptEyOloyAlIiIlkTsj5U0Uvqt5hr968Mo9BSkpNgUpEREpicwVewYW7pi9z56rgM04M/w1OdvEDPRhpRt/ihSDgpSIiJREpodUjRHDsFIAGAXcHiajtmaHppz9vQV/D5EMBSkRESmJTFfzJvdA9r5iLe31DQlSWt6T4lGQEhGRksgs7U2sHiw6L2Qzzgw15ZRSUpASEZGSyCztteZuD1OUILXj0p56SUnxKEiJiEhJZJb2creHMYpUbB62KklZBqCNi6W4FKRERKQkQumlvYZMjVSlr6BdzTNqq71YuAilr9wzNSMlRaQgJSIiRWdZVrYhpx97exhXgZtxZvhr7HCWqZPSjJQUk4KUiIgUXSyRIp40AfClt4cxCrw9TIa/xgugppxSEgpSIiJSdH05Xc0rU3YzzmLURwH4qrwYBtltYkwFKSkiTz4vDgQC/wR8O/3lY8Fg8Jv5D0lERPY2mSv2DCy8CXufvWIt7blcBr6qwW1iiEWwkvGi1GOJjHlGKhAI1AA/A04CjgBODAQCpxdqYCIisvfI9JCqNaIYlr3EV4zWBxk79pLS8p4USz5Le+70632AN/3fwLCvEBGRfVJmw+I6V3/2vmLVSEG6l5Q12EtKy3tSLGMOUsFgMAR8F3gH2AR8ALxUmGGJiMjeJNP6oN41+O/tYnQ1z/DX7LBNjK7ckyIZc41UIBA4HLgcmAH0AvcC3wT+cySvb26uHetbj1hrq7/o7yFD6ZyXls53ael8j10Kuzlmkyeava952hS89bs/p/mc79YmH+/kLO35XAPU6/s3LP18j00+xeZnAk8Fg8FtAIFA4E7gS4wwSHV1hTFNK4+3H15rq5+OjlDRji870zkvLZ3v0tL5zs/WTrvlQUvFYFfz7QMejPiuz2m+59tjQMSqJGm58BgmfVvbiev7t1v6+d49l8sYdvInnyD1BvCjQCDgA/qBs4EVeRxPRET2UqEBe2mvyRsFE4wqP4bbW7T3s3tJGfSa1TS7Iyo2l6LJp0bqCeAB4BXgTexi8xsLNC4REdmLZIrNG9I1UsW8Yg8Gm3L2qSmnFFlefaSCweAPgR8WaCwiIrKXCqeLzf1Guqt5kZpxZvir09vEWJltYrTfnhSHOpuLiEjRZWakasxMkCpOM86MHbeJUfsDKRYFKRERKapY3N5nz8CkMmUHKVcRe0jB4MbFmW1iSESx4mp1KIWnICUiIkUVyi7rRTGwr9Yudo1UbfXQGSkAq7+3qO8p+yYFKRERKarQQKar+eCMULGDlNfjorrSPWSbGLNfdVJSeApSIiJSVINdzQe3hyn20h7Ys1JDZ6RUJyWFpyAlIiJFNbjPXulmpMCuk+qztE2MFJeClIiIFFUmSOXOSBW7/QGAv9rLgOUlke70oyv3pBgUpEREpKgyS3vZZpzVdRiuvNoYjoh95Z6RnZVSLykpBgUpEREpqsyMVJPX3rC4FLNRALXpXlI9qXRTTs1ISREoSImISFHtNCNV5GacGf4dgpSW9qQYFKRERKSoMu0Pag27RspVgkJzGNwmpi9nmxjLskry3rLvUJASEZGiCvXHcWFSY9lByihB6wPYeZsYUgmI9w/zCpHRU5ASEZGiCvUn0l3NbaVofQCDNVJ9Q5pyqru5FJaClIiIFE0imSIaT+3Q+qBUM1I77LeHCs6l8BSkRESkaHbVjLN0NVI7z0gpSEmhKUiJiEjR7LoZZ2mCVFWFG4/bNbS7uZb2pMAUpEREpGgyrQ8GZ6QMjJq6kry3YRj4a+zu5kl1N5ciUZASEZGiyS7tGekeUlW1JelqnmEv7xn0u9LdzTUjJQWmICUiIkWz44xUqZb1MjItEMKZbWL6tU2MFJaClIiIFE2mGWemRqpUPaQyMlfu9ZiZ7uaakZLCUpASEZGiycxI1bvT++xVlzZI1aav3NueqAJ01Z4UnoKUiIgUTag/gYFJbbpGylWiDYszMkt73Uk7SJGIYiViJR2D7N0UpEREpGhC/QlqjRgu7D3uSl8jpaacUlwKUiIiUjSh/vjQHlIlr5FKN+W0creJUZCSwlGQEhGRogn1Jxzpap4xOCOlppxSHApSIiJSFMmUSX8sOSRIGSWukcoUm/dqaU+KREFKRESKIjwwtBkngFHtTLF5v1WJmf6VpyAlhaQgJSIiRbHTPnuVPgxPRUnH4Kv2YhhgYRDz1AKqkZLCUpASEZGi2LGreanrowBchpFd3htw+QDVSElhKUiJiEhRZPfZc2h7mIxMkAqT2SZGM1JSOApSIiJSFNmu5kZ6e5gSF5pn7NhLSkt7UkgKUiIiUhR2V3MLv8veHsaJpT0YLDjfnuluHotgpRKOjEX2PgpSIiJSFKGBBDVGDI9hAs4t7WVmpDrjldn7VCclhaIgJSIiRWF3Nc/tIeVQkErXSHXEcoOUlvekMBSkRESkKOyu5jnbwzhUI1Xns2ekcptympqRkgJRkBIRkaII9ceHNON0+RodGUe9TxsXS/EoSImISFGE+hM7LO05OyMVsqqwMAAFKSkcBSkRESk407SIDOQs7XmrMTyVw7+oSDJBysJF0mt3N1eQkkLx5PPiQCBwNvCvgA94IhgMfrUgoxIRkXEtHE1gkdvV3JnZKIC6msFtaWKeWryJkGqkpGDGPCMVCAT2A34FnAscDswNBAILCzUwEREZv7JdzdM1UoZD9VEA1ZVuPG77112/oe7mUlj5LO19EvifYDC4KRgMJoALgeWFGZaIiIxn4UxX8+z2MM7NSBmGQb3PboEQshSkpLDyWdrbH4gHAoE/AdOBR4DvFmRUIiIyrtkzUla2RsqpHlIZdb4Kuvpi9KbsK/esgRCWmcJwuR0dl4x/+QQpDzAfOBkIA38CLgHuHMmLm5tr83jrkWlt9Rf9PWQonfPS0vkuLZ3vkTPXdFJtxPGmu5r7WyfSMMrzV8jz3dJYw/tbQmzPtkCwaKox8fidDXjlRD/fY5NPkGoH/hYMBjsAAoHAw8CxjDBIdXWFMU0rj7cfXmurn46OUNGOLzvTOS8tne/S0vkenS3bQkN6SPVbVSRGcf4Kfb6rvXYly9YBL9irfHRu3Iy71Vuw9xjP9PO9ey6XMezkTz5B6hHgrkAg0ACEgIXAH/I4noiI7CXKZXuYjEwLhNwgpTopKYQxF5sHg8HlwI+AF4BVwHpgcYHGJSIi49iO28O4nA5SNbvaJkZBSvKXVx+pYDD4G+A3BRqLiIjsJUL9cSaX4YyUtomRQlNncxERKbjQQM72MJ4K8FY5Op7Mfnsp3KS8PkBBSgpDQUpERAou1J8YbMZZ04hhGI6OJzMjBZDIbhOj7uaSPwUpEREpKNOyCOfUSDm5PUxGbpAacNlBSjVSUggKUiIiUlD90SSmZeV0NXe+V1NNpQeP254Vi2S3idGMlORPQUpERAoqlN4epq4MtofJMAwDf/rKvT5rMEhZlunksGQvoCAlIiIFFepPUEmCSiMJ2DVS5SBTcN6TTBe+WymsaNjBEcneQEFKREQKKtSfoH5IDynnZ6RgsE6qK16ZvU9X7km+FKRERKSgQv3x7LIelEeNFOR0N48NFp4rSEm+FKRERKSgesKxsgxSmaW99v7B/fVUcC75UpASEZGC6o0MnZFy+cojSGW2ielJaZsYKRwFKRERKajecJw6I10j5fZARY2zA0rLLO0l8GB57IJzLe1JvhSkRESkoHrCsSE9pJzuap6R25QzWVEHaGlP8qcgJSIiBZW7tFcu9VEwNEjFvOpuLoWhICUiIgVjWpa9tJcOUq4yClL1u9gmRjNSki8FKRERKZhQfwLTsrI1UuXQ1TyjpsqD22UvM4bJdDfvwbIsJ4cl45yClIiIFExvOIaXJDWuBFBeS3suw8gu7/Wm0t3NUwmI9w/zKpHhKUiJiEjB9IR3aH1QRkEKBlsgdCcHryQ0I9udGo7sBRSkRESkYHrDsSHbw5TTjBQMFpxvi1Vl77PCXU4NR/YCClIiIlIwPZE4dUb5dTXPqPPZXc23RAf32zPD3U4NR/YCClIiIlIwveEYDbkzUmXS1TwjMyO1OeKBdH8rK6IgJWOnICUiIgXTG47T6I7YX7grMCprnR3QDurTNVIJ04BqO+SZWtqTPChIiYhIwfREYjS47CDlqm0qm67mGUO6m1fZQcrS0p7kQUFKREQKpicUpzEdpIzaZodHs7PcIBWvSM9IaWlP8qAgJSIiBWFZFr2RWDZIuco8SPW7/YA9I2VZplNDknFOQUpERAoiEk1CKkmdKwqAUdvk8Ih2lrtNTJh0/ZaZxBoIOTQiGe8UpEREpCDsK/Yi2a/LcUbKV+3Fla7b2m75svfryj0ZKwUpEREpiJ5IfGjrgzIMUi7DwJ/uJdWZ291cV+7JGClIiYhIQfSGB+ujwL5qrxxlWiAM7W6uGSkZGwUpEREpiN5wfEiQMnzlGaSy28T0u8HtAXTlnoydgpSIiBRETzhOoysMgFHlx/BU7OEVzsgEqb6BBIbPXn7UfnsyVgpSIiJSED3hGI3pGqlyrI/KyAapSByXrxHQfnsydgpSIiJSEL3hWHZ7mHK8Yi+jLl0jlUxZmDV2kNJVezJWClIiIlIQPTnNOMuxh1RGbi+pmLceACvSg2UmnRqSjGMKUiIiUhDxcJhKww4jZT0jtYvu5mBhRXqcGZCMawpSIiKSt4FYEp/Zl/16vMxI9WW6m6Mr92RsFKRERCRvvZF42Xc1z8idkeoxc7qb68o9GQMFKRERyduOzTjL+aq92mov6V1iduhurhkpGT0FKRERyVtPTjNOy3BjVNc5PKLdc7kM/Okr97ZHDfBWA+puLmOTd5AKBAI3BQKBOwswFhERGad6cmakDF8ThlHe/07PtEDoiySyy5Dab0/GIq+f9EAgcBpwSYHGIiIi41Tu9jAuf/kWmmfUpzcu7o3Es4Xx6iUlYzHmIBUIBJqAfwd+ULjhiIjIeJTbQ6qcC80zhnY3TwcpLe3JGOQzI/Vr4DvA9gKNRURExqm+UJR61wAwzoJUf86MVCyMlYw5OSwZhzxjeVEgELgS2BgMBp8KBAKXjuUYzc21e35Snlpb/Xt+khSUznlp6XyXls73MKI9uAwLgLq2ydQV4FwV83xPnmAfO5E0qWppI56+v6EiRkVzS9Het5zp53tsxhSkgAuBSYFA4HWgCagNBAL/FQwGvz7SA3R1hTFNa4xvv2etrX46OkJFO77sTOe8tHS+S0vne3hWqAvsi9+IWD5ieZ6rYp9vjzF4e0vES6abVNeGjXjM8r3isFj08717Lpcx7OTPmIJUMBj8eOZ2ekbq5NGEKBER2XvEEylqUrldzct/aa+5rip7uztZkw1Sasopo1Xe16eKiEjZs7ua92e/dpXx9jAZLfWDQWpbfPC2tomR0Rrr0l5WMBi8E7gz75GIiMi4lNtDKuWpxqiodnhEe9ZQW4nbZZAyLTpDSYzqOqyBPs1IyahpRkpERPKS20PKqml0eDQj43IZNPorAejqi2aXI7VNjIyWgpSIiOQld0bKPQ7qozIydVJdvdHBXlJa2pNRUpASEZG82DVSdpDy1o+f1gHN6Tqpzt6BbC8pM9yFZRXvinLZ+yhIiYhIXsJ9ffhcdicml3/8zEhlCs57w/HBJclkHGIRB0cl442ClIiI5CUVGlwOGw9dzTMyS3sW0O8abEapK/dkNBSkREQkP/2DO4WNhx5SGc05LRB6TF/2tq7ck9FQkBIRkbx4Y4NBKlO0PR7kBqmO5GDLBl25J6OhICUiImOWTJlUJ+2u5hYGhq/B4RGNXJN/MEi193vBcAO6ck9GR0FKRETGrC8y2EMq4a3DcOXd57lkvB4X9bUVAHT1xbMh0NTSnoyCgpSIiIxZT04zzlT1+JmNymjJ9JLqi2YL5S0t7ckoKEiJiMiY9eY04xxPV+xlDPaSimKk67t01Z6MhoKUiIiMWU84mt2w2FM3foPU9lAMw2f3krLC27FM08lhyTiiICUiImPW37Mdj2GHjqrGCQ6PZvQyS3sp0yLqrbfvtFJYA70OjkrGEwUpEREZs4HubdnbHv/42R4mI7cFQh+12dvqJSUjpSAlIiJjlujrzN7O7Fc3nmS6mwN0mjndzXu3OjEcGYcUpEREZMyM/vG5PUxG7ozUlpgPDPvXotmzxakhyTijICUiImMSHkhQb/YAkHRVQKVvD68oP1UVHnxVdu+rznASo64VUJCSkVOQEhGRMenoGWCi2y7KTvomYhiGwyMam5Z6e3uYrt4orvpJgIKUjJyClIiIjMnW7f3ZIOVqmOTwaMYus7zX1RfNfg6zbyuWmXRyWDJOKEiJiMiYdHd2U+eKAlDdOs3h0YxdpuC8qzeKq6HNvtNMYeUU0ovsjoKUiIiMSaxzc/a2t2WKgyPJT2ZGKp40iVYN9sLS8p6MhIKUiIiMidE7GDTcDZMdHEl+clsgdBuD+wWmFKRkBBSkRERkTCoHOgBI4c5e7TYeteS0QOgccGNU2f2kNCMlI6EgJSIiozYQS9Jo2j2kopVNGC63wyMau9xeUp29OQXnvQpSsmcKUiIiMmrbtg+2Pkj52xweTX58VR4qK+wgOOTKvZ4tWJbl5NBkHFCQEhGRUevo6qPJFQbA2zR+C80BDMPIbl7clTMjRSyCFQ05ODIZDxSkRERk1MJbN+JK99+smTB+Wx9kZJb3cpf2QHVSsmcKUiIiMmqJ7sHWB9UTpjo4ksLI9pLqU5CS0VGQEhGRUXOHtgJgwWATy3EsMyM1EEsy4GkAt73/noKU7ImClIiIjFp11G59EHHXY3gqHR5N/ob0kgrHcdXb4VBBSvZEQUpEREYlFk/RZG23b1eP3/5RuXJ7SeUWnCtIyZ4oSImIyKh0dIeZ4O4DwKob/8t6MLSXVG6dlBXqxErGnRqWjAMKUiIiMirdWzbjMUwAKlvGf6E5QJ2vAo/bvgyxs3cgp+Dcwuzd6tzApOwpSImIyKhEOzZlb/snzXBwJIXjMgyadtVLCi3vyfAUpEREZFRSPR9mb9dOHP89pDKGtECoH1yyVJCS4ShIiYjIqHjD9lJXhGqMqlqHR1M4mTqprt4ohrcKw9cEKEjJ8BSkRERkVGoTnQCEvS0Oj6SwMtvE9PUniCdSunJPRkRBSkRERiyeSNFMDwAJ3wSHR1NYu7tyz+zdgmWZTg1LypwnnxcHAoF/BT6V/vLRYDD4v/IfkoiIlKvure34jAQARk5B9t6gtaE6e3tLVz/Nmc+XjGNFtmPUNjs0MilnY56RCgQCpwNnAEcBRwJHBwKBTxZqYCIiUn56P9yQvV3TuvcUmgNMmzBY77Vha0hX7smI5LO0twW4NhgMxoPBYAJYDUwvzLBERKQcxToHWx80TJ3p3ECKoLrSw8RGe1ZqfbuClIzMmJf2gsHg25nbgUDgAOwlvhMKMSgRESlTvXagiFpempv3ju1hcs1o87N1+wAbtoUxahrAWwWJqIKU7FZeNVIAgUDgUOBR4FvBYHDtSF/X3Fz8S2ZbW/1Ffw8ZSue8tHS+S0vnG6rSmxX3uBs5ZGJ9Ud/LifN98H4t/H31NraHYnirK6hsmUJsy7u4+zv2+u//3v75iiXfYvMTgN8DXwsGg78dzWu7usKYppXP2w+rtdVPR0eoaMeXnemcl5bOd2npfNv88S4wIFLRUtTz4dT5bqmtyN5+bVU7+/smAO8S27Zxr/7+6+d791wuY9jJn3yKzacBfwA+M9oQJSIi40+iP0yt0Q+AWTvR4dEUx/SJuy44t/p7sOIDTg1Lylg+xebfBKqAnwQCgdfT/11doHGJiEiZ6fnwg+xtT9MU5wZSRP6aCprqKgEVnMvI5FNs/lXgqwUci4iIlLHwlg1kWlb69qI99nY0Y6Kf7r4Y67eGcDUObsqc6t6Ie8J+Do5MypE6m4uIyIgkuu3NipOWi+Ype3eQAujoiRKtbIEKuyVCassaJ4clZUpBSkRERqSidz0A28x66v3Ve3j2+DV94uDVaxs7+nG3HQhAqj3o1JCkjClIiYjIHlnJOA3RzQBs9U7FMAyHR1Q8M9oGg9T6rSHcbQEArFAnZrjLqWFJmVKQEhGRPYptXoMbe+PeZMsBDo+muBpqK6ir8QJ2kPJMDmQfS23RrJQMpSAlIiJ71L3ujezthtlzHBxJ8RmGwfT0rNSGrWFcLTPAY1/Jl9ryjpNDkzKkICUiInuUmYnZnGxk9qzJDo+m+DIF51u6IsSTBu6J+wOQVMG57EBBSkREhmUlY/j77c2KN7unUF9b6fCIii8TpCwLNnaEcU9K10n1tmP29zg5NCkzClIiIjKs5Idrs/VRiea9uz4qY3pOwfmGraFskAK1QZChFKRERGRY2999EwDTgrpZhzo8mtJora+iutLuWb2+PYS7dRa47a9VJyW5FKRERGRYyQ9XA/Bhat+ojwK74HxGet+99VtDGJ4K3BNmA5qRkqEUpEREZLesRBRfxO4ftZ4pTGjcextx7ijTmHNzR4Rkyswu75nbN2FGQ04OTcqIgpSIiOxWcssaXOn6qFjT7L26EeeOMgXnKdNic0cE96SDso+l2jUrJTYFKRER2a3QBysBuz7KP2PfqI/KmL5jh/MJs8FwA5D6UI05xaYgJSIiuxXfZNdHbU41MXvWJIdHU1qTmmqo8Ni/JtdvDWF4K3G1zgS0754MUpASEZFdsuIDVIft/lHvmZOYOsHn8IhKy+UymDbBLjjfsNWuifJk6qS6NmDF+x0bm5QPBSkREdmlVPtaXFgADDTMxu3a935lZJb3Nm4NY5rWYD8pyyLVvtbBkUm52Pf+VIiIyIj0b3gbANMyqJl+sMOjcUam4DyeNNnS3Y+77QBIF9xrA2MBBSkREdmN2MZVAGxKNTF7iLRd4AAADd1JREFURpvDo3FGJkgBrN3Yg1FRg6t5OgBJBSlBQUpERHbBig9QGbLro9Yl25g1uc7hETlj2oRa6msrAFi2aitAtg2C2fEBViLm2NikPChIiYjITlLtQYx0fVTIP4tKr9vhETnD5TL42CETAVizsYfO3gHckw60H7RSpLauc3B0Ug4UpEREZCexjXbbg5RlUDNt36yPyjju0MFlzeWrtuJpCwB2nVTyg1ccGpWUCwUpEREZwjJN4u+tAGBjqpn9Zkx0eETOmjahlimtduuHl1a2Q6UP91S7OWlizYtYsYiTwxOHKUiJiMgQyQ9ewTPQDcDLsf3Yf2q9wyNylmEY2VmpLV39bNgapuKwM+wHkzESwecdHJ04TUFKRESyLMsi/uZjAETMCjbWHk5ttdfhUTkvUycFsPTtdtzTDsOot8NV/O2/YZmmU0MThylIiYhIVmrrOsxt7wHwYizA4QdNdnhE5aGproqDpjcA9tV7pgUVh50OgBXqJLnhNSeHJw5SkBIRkazEm38FIGm5WJo8mFOPnurwiMpHZnmvLxJn9Qfb8R44DyqqAUi89aSTQxMHKUiJiAgAZu9WEh+8CsDL8VkcMWc2dTUVDo+qfBwdmIDHbf/aXPp2O4a3Cm9gPgCpLe+Q6tro5PDEIQpSIiICQPytx7O9o56NHsqZx053eETlpabKw5EHtADwypoOovEkFYeeTqYVQmKlZqX2RQpSIiKCFQ0TT199tio+mWkHHsiEhmqHR1V+jk8v78UTJq+t6cRV14pnxpEAJNYtxYyGnByeOEBBSkREiK96GiOVAOCZ6CEs/OgMh0dUng7bryl7FePSt9sB8M5Jt0JIJUisftahkYlTFKRERPZxVjJOfOXfANiUbMQ75RBmtPn38Kp9k8ft4iMHTwDg7Q+66Q3HcE86CFfTNAASq57GMpNODlFKTEFKRGQfl1y3DKJ9gD0bteC4mc4OqMxllvcsCx5duh7DMPBmWiFEtpNct9zJ4UmJKUiJiOzDzMh2oq/8AYAes5quhjkcMqPR4VGVt/0m1zFrUh0Af3tlEyve2YZ3/+MwquxZvOiL9+gKvn2IgpSIyD7KikUY+MuPIWJvB/PkwBzOPG4WhmE4PLLyZhgGV59zKDWVHgB+85fVtPcmqJz3OfsJiSgDf/0vzMh2B0cppaIgJSKyD7KScQYevxlz+yYAno8GCFYfwdGBVodHNj60NlRz1dmHABCLp/jFwytJTT2Kyo9eCIAV6Wbgr/+FFR9wcphSAgpSIiL7GMtMEX3ql6Ta1wDwWnwGv+//COedtD9ul34tjNQR+7ew6PiZAHzYGeHOx97BM+dMvIecCoDZtYGBp36JZaYcHKUUm/7EiIjsQyzLIvb8nSTX23vDrUm0cW94HpcsPIRjD564h1fLjs6dN4tDZ9o1ZX9fvY2nX91M5fEX4552OACpjW8Se/FeLMtycphSRApSIiL7CDMaIvbCXSTSjTc3Jpv4TfgULj97DvOP0ObEY+FyGXz+Hw6lqa4SgP95eh0vrtxG5alfxNVs9+JKrH6G6LO3Y4a7nByqFImClIjIXs7s7yG67LdE7v9mtmFkR8rPbZHTufzcuXwsfTm/jI2/poIvnnsYbpdByrT4zV9W86/3vMnaAz6L4bNnq5JrXyTy2+uIvnCPitD3Mp58XhwIBD4D/AvgBX4aDAZ/UZBRiYhIXizTxOzZQnzV0yTeeQ4jp0nk+8kWHhg4icv+8aMcPrvZwVHuPWZPrueL5x7GPU8E6Q3H+bAzws/+EuGIiZ/gotbXqOl4G8wkiVVPkQguwXvIqXgPOB5X0xQMV16/isVhY/7uBQKBKcC/A0f///buPcaKs4zj+HfOZReWBYRly60UtiU8NC03hTYVqf5hNBiEplWb1MRqL8R4/VMT26Rq1GisbTQ2MSFqtWI0JUo0bWmU2ouoRQkXQ3nSVi4CCwWCBZa9n/GPmQ2HZcsZZndnOZPfJ9nsXM7Z8+yT98z7nHfeMwN0A9vM7AV33ztSwYmIyNDCMIT+HsLu84Td56h0dtBx4gjdx/bD6UM0nmunGEa3fBm4mMEbvdPZ0rmI4+Pmsv5jN3Ojrhc1ot69oJWb2qaydcdhnvnbQTq6+th1vMCu4+9h/rg21jbvZm7lUHQrmT1b6N2zBQolCi1zKLa2UZw2j2DiNIJxzQSNzQTjJhCUGsf635IagrQT4MzsXuB2d78/Xn8YCNz9GzWeOg/Yf+rUOSqV0Zl899pLz1N8/UXQZfozFQSBJlRmSPnO1kjne+grNYXx9uh3QAWAQlihQIUC/RSJlhvCHkpBJdFrvdY7k63di5l0/SJW3jyDm9qmUipe3TM7WlsncuJE/d4A+HxXH89vP8SW7f+lu+fCt/auLx1n9fhdLCgfS/R3einSR5n+gRYQFKlQJCSo+gGqfg+WpNXW6/GkUihTWvIR5i9/76i9RqEQ0NLSDNAGHBi8fzjjibOA9qr1duCWpE+OgxoVB/Y9Sws6B525+nsP1jflO1tXW77f4ZqZPWGRI/1TONI3lZPFa+id2sbi5Uv4+tLZNDc1ZBvjMLW21vf9/h6cM4VPfGgh2/a0s//I2/zn6NscbC/y47PTaS2cYW7pJHNKp7iueJLZpdM0Bpd++C/TT5mqyyeMVju82tp3Uv1wdM9ztK7+8JiFMJxCqsDFqQ+AZB+PgNEckepZdAeH/UXdODJjhSCgUoefaOqV8p2t0cn3hWoovGjboJGGoEAlKBIGBcKgSCUoUCk00lcaT6XcRFhugoYmChOm0Dz9Wqa9q4kFk8cxruHCIb6zo5vOju4Rjn/01PuIVLXl81tYPj+ai1YJQ06c7uTIyQ46unrp7O7nQHcf+7p6KHa8Rbn3HOVKJ+X+Lhr6z1OudFIM+yiE8ZhU2B8vh1wYuYyWGXJMKlmbrdfjSRiUaVq2elTbStWI1JCGU0gdBlZVrc8Ajg7j742YBbe9n9a1a3LzJqwXeTrw1QPlO1vKt4yEQhAwfWoT06c2DbHXMo9ngNp3esMppP4EPGJmrUAHcBewfkSiEhEREakDqWcbuvsR4GvAC8BOYKO7vzpSgYmIiIhc7YZ18Qp33whsHKFYREREROrK1f39VxEREZGrmAopERERkZRUSImIiIikpEJKREREJCUVUiIiIiIpqZASERERSUmFlIiIiEhKKqREREREUhrWBTlTKkJ0E8DRlsVryMWU82wp39lSvrOlfGdL+R5aVV6KQ+0Pwuzv9vw+4OWsX1RERERkGFYBrwzeOBaFVCOwAmgH+rN+cREREZErUARmAtuB7sE7x6KQEhEREckFTTYXERERSUmFlIiIiEhKKqREREREUlIhJSIiIpKSCikRERGRlFRIiYiIiKSkQkpEREQkpbG4RcyIMrOvAp8hukjWb9z9W4P2Xwc8BVwDOPBJdz+XeaA5kSDfK4HHgAbgFHCfux/MPNCcqJXvqsctA/7u7o1ZxpdHCdr4TGADMAs4T3RMOZB1nHmRIN/zgF8Ak4D/AffqmHLlzGwSsA1Y4+4HzOyDwA+A8UR5f2iI56j/TKCuR6TihnAP0ZXSlwG3mtmdgx72BPCEuy8E/gk8nG2U+ZEw378CHnD3pfHyD7ONMj8S5hszawJ+RFS8yjAkzPkvgT+4+7J4+bvZRpkfCfP9TeDX8TFlEzDkhwl5Z2Z2K9GtTRbE6+OBnwLrgBuBFWa2eoinqv9MoK4LKaI33hZ3P+Pu/cBzwB0DO82sDNwOPB1v+jnw8ayDzJFa+W4EHnL33fGm3cB12YeZG5fNd5VHgcczjSy/arXxacAS4Cfxpp8Bl3ySl8SStPEi0WgUwASgM8P48uJB4PPA0Xj9FuB1d9/v7n1Eo04X9Y3qP5Or91N7O4DHzOw7REPsa7m4OJwGnIkbCkT397s22xBz5bL5dvduojckZlYAHgF+n32YuVGrfWNma4Emd3/azMYgxNyplfMbgEPAo2a2CjgGfCHzKPOjZhsnGgXZZmZfIhp1vS3bEOufuz8AUHWMmEXUHw4Yqm9U/5lQXY9IufufiarkvxB9knkF6Kl6SAEYfDPBShax5VGCfANgZg1Ep/VKwLezizBfauXbzGYQjYZ8cQzCy6UEbbxENIqy1d1XAJuBJ7ONMj8SHlOeBNa7+2zgs8DvzCzIMMw8Gtw3BlzaN6r/TKiuCykzmwhscvfF7v4BosmKb1Y95C1gspkV4/WZXBjalCuUIN+YWTPRAbEErHP33swDzYkE+V4DtAAvmdnO+Dk74+dJCglyfgw46+5/jNc3Ep0mkRRq5dvMWoGF7r4ZwN03ATOIRkskvcNE/eGAGVzaN6r/TKiuCymgDdhsZiUzmwzcD/x2YGfcib8M3B1v+hTwbOZR5sdl8x17CngDuDs+1Sfp1WrfG9z9BndfGk/EJV4+O0bx5kGtnL8JHK6amPtR4F/Zh5kbtY4pJ4Gu+DTqwLeCz7r7iexDzZV/AGZm8+NC6R4G9Y3qP5Or60IqntS8iWhS86vA4+7+VzPbEM8dAfgcsN7M9gKr0MTQ1GrlO/4K/jpgJbAjHh15ZgxDrmsJ27eMoIQ5vxP4ipn9G/gycN/YRFv/auXb3UOifH/fzHYD3wPuGruI88Hdu4BPE+V+L7CPeFK5+s8rF4Th4FOgIiIiIpJEXY9IiYiIiIwlFVIiIiIiKamQEhEREUlJhZSIiIhISiqkRERERFJSISUiIiKSkgopERERkZRUSImIiIik9H9jdM6YxnFo7gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare the VI posterior with the analytical distribution\n",
    "xs = np.linspace(9, 10.1, 100)\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(xs, st.norm(loc=gtilde, scale=np.sqrt(s2tilde)).pdf(xs), label='True Posterior', linewidth=2.5)\n",
    "plt.plot(xs, gpost.pdf(xs), label='VI Posterior', linewidth=2.5)\n",
    "plt.legend(loc='best', fontsize=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see our approximation of the posterior is not exact, but close. The normal-normal model is a very simple example with 1 latent variable.  In practice setting up the variational posterior for all latent variables, keeping track of transformations and optimizing the variational parameters can become highly tedious for models of any reasonable level of complexity. From this point on, we will use `PyMC3`'s ADVI capabilities.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2 - Coin-toss example \n",
    "\n",
    "Just like in the MCMC lecture, let's look at the process of setting up a model and performing variational inference and diagnostics with the coin toss example.  \n",
    "\n",
    "The probabilistic model is as follows. We observe binary coin toss data:\n",
    "$$\n",
    "x_i|\\theta \\overset{\\mathrm{i.i.d.}}{\\sim} \\mathrm{Bernoulli}(\\theta),\n",
    "$$\n",
    "for $i=1, \\dots, N$.\n",
    "\n",
    "The prior over the latent variable $\\theta$ is a Beta distribution:\n",
    "$$\n",
    "\\theta \\sim \\mathrm{Beta}([2, 2]).\n",
    "$$\n",
    "We assign the prior as a Beta distribution with shape parameters 2 and 2, corresponding to a weak apriori belief that the coin is most likely fair."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetaprior = st.beta(2., 2.)\n",
    "x = np.linspace(0.001, 0.999, 1000)\n",
    "plt.plot(x, thetaprior.pdf(x), linewidth=2.5)\n",
    "plt.title('Prior');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We wish to perform posterior inference on $\\theta$:\n",
    "$$\n",
    "p(\\theta| x_1, \\dots, x_N) \\propto p(\\theta) \\prod_{i=1}^{N} p(x_i | \\theta).\n",
    "$$\n",
    "Since this is a conjugate model, we know the posterior in closed form:\n",
    "$$\n",
    "\\theta | x_1, \\dots, x_N = \\mathrm{Beta}(\\theta, 2+ \\sum_{i=1}^N x_i, 2 + N - \\sum_{i=1}^Nx_i )\n",
    "$$\n",
    "\n",
    "Let's generate some fake data and get the analytical posterior for comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetatrue =0.3\n",
    "N = 25\n",
    "data = np.random.binomial(1, thetatrue, size=(N,))\n",
    "nheads = data.sum()\n",
    "ntails = N - nheads\n",
    "theta_post = st.beta(2. + nheads, 2. + ntails)\n",
    "\n",
    "# plot data \n",
    "plt.figure(figsize=(12, 5))\n",
    "plt.subplot(121)\n",
    "_=plt.bar(*np.unique(data, return_counts=True), width=0.2)\n",
    "_=plt.xticks([0, 1], fontsize=15)\n",
    "_=plt.title('Observed H/T frequencies', fontsize = 15)\n",
    "\n",
    "# plot posterior\n",
    "plt.subplot(122)\n",
    "x = np.linspace(0.001, 0.999, 1000)\n",
    "postpdf = theta_post.pdf(x)\n",
    "y = np.linspace(0., np.max(postpdf), 100)\n",
    "plt.plot(x, postpdf, linewidth=2.5, label='Posterior')\n",
    "plt.plot(x, thetaprior.pdf(x), linewidth=2.5, label='Prior')\n",
    "plt.plot(thetatrue*np.ones_like(y), y, linewidth=2.5, linestyle='--', label='True $\\\\theta$')\n",
    "plt.legend(loc='best', fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.title('Coin Toss Bayesian Inference', fontsize = 15);\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's setup the `PyMC3` model and do variational inference. To do this, we simply need to setup the model like in the MCMC setup, and call `pymc3.variational.ADVI` to do inference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "            \\begin{array}{rcl}\n",
       "            \\text{theta} &\\sim & \\text{Beta}(\\mathit{alpha}=2.0,~\\mathit{beta}=2.0)\\\\\\text{x} &\\sim & \\text{Bernoulli}(\\mathit{p}=\\text{theta})\n",
       "            \\end{array}\n",
       "            $$"
      ],
      "text/plain": [
       "<pymc3.model.Model at 0x13fd7dc88>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = pm.Model()\n",
    "with model:\n",
    "    theta = pm.Beta('theta', 2., 2.)\n",
    "    x = pm.Bernoulli('x', theta, observed=data)\n",
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 16.902: 100%|██████████| 20000/20000 [00:14<00:00, 1359.17it/s]\n",
      "Finished [100%]: Average Loss = 16.902\n"
     ]
    }
   ],
   "source": [
    "num_iter = 20000\n",
    "num_samples = 20\n",
    "with model:\n",
    "    method = pm.ADVI()  # <- This method makes q a diagonal Gaussian\n",
    "    #method = pm.FullRankADVI() # <- this method makes q a Gaussian with full rank cov. matrix\n",
    "    #method = pm.SVGD() # <- Stein Variational Gradient descent (see additional readings)\n",
    "    #method = pm.NFVI() # <- Normalizing flow Variational inference (see additional readings)\n",
    "    vi_approx = pm.fit(n=num_iter, \n",
    "                       method=method,\n",
    "                       progressbar=True, \n",
    "                       obj_n_mc=num_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's check the optimization convergence \n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(np.arange(num_iter), -vi_approx.hist)\n",
    "plt.ylabel('ELBO', fontsize=15)\n",
    "plt.xlabel('Iteration', fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.xticks(fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, we see that the optimization has converged. \n",
    "\n",
    "Recall that ADVI transforms every variable with finite support with an invertible function to obtain a variable with support over the entire $\\mathbb{R}$. The variational posterior is then set to be a diagonal Gaussian. \n",
    "In the coin toss problem, the latent variable $\\theta \\in (0, 1)$ is transformed with the logit function $g(\\theta ) = \\log \\frac{\\theta}{1 - \\theta}$, i.e., `PyMC3` works with the transformed variable $\\tilde{\\theta} = g(\\theta)$. \n",
    "The posterior over $\\tilde{\\theta}$ is then approximated with a Gaussian $q_{\\phi}(\\tilde{\\theta}) = \\mathcal{N}(\\mu, \\sigma^2)$, where, $\\phi = (\\mu, \\sigma)$ are the variational parameters. Let's get these parameters and visualize the posterior. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the variational parameters a\n",
    "mu, sigma = vi_approx.mean.eval(), vi_approx.std.eval()\n",
    "qtheta_transformed = pm.Normal.dist(mu, sigma)\n",
    "transform = pm.transforms.logodds\n",
    "def qthetalogp(x):\n",
    "    x = tt.as_tensor(x)\n",
    "    y = transform.forward(x)\n",
    "    logpy = qtheta_transformed.logp(y)\n",
    "    logpx = logpy + transform.jacobian_det(x)\n",
    "    return logpx.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0.001, 0.999, 1000)\n",
    "postpdf = theta_post.pdf(x)\n",
    "postpdf_vi = np.exp(qthetalogp(x))\n",
    "y = np.linspace(0., np.max(postpdf_vi), 100)\n",
    "plt.plot(x, postpdf_vi, linewidth=2.5, label='Posterior (ADVI)')\n",
    "plt.plot(thetatrue*np.ones_like(y), y, linewidth=2.5, linestyle='--', label='True $\\\\theta$')\n",
    "plt.legend(loc='best', fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.title('Coin Toss Variational Bayesian Inference', fontsize = 15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Posterior predictive distribution\n",
    "\n",
    "To estimate posterior predictive expectations, we first create a `MultiTrace` object out of the results of the ADVI stored in `vi_approx`.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "trace = vi_approx.sample(2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this point all of the computation is exactly as it was when doing MCMC. Let's generate some synthetic datasets from the posterior predictive distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rohitkt10/anaconda3/lib/python3.6/site-packages/pymc3/sampling.py:1247: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample\n",
      "  \"samples parameter is smaller than nchains times ndraws, some draws \"\n",
      "100%|██████████| 500/500 [00:00<00:00, 2854.66it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(500, 25)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_samples = pm.sample_posterior_predictive(trace=trace, samples=500, model=model)\n",
    "x_post = pp_samples['x']\n",
    "x_post.shape # num samples of theta \\times size of the dataset "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 20 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10, 10) )\n",
    "for i in range(20):\n",
    "    plt.subplot(5, 4, i+1)\n",
    "    plt.bar(*np.unique(x_post[i], return_counts=True), width=0.2)\n",
    "    plt.bar(*np.unique(data, return_counts=True), width=0.12, \n",
    "            alpha=0.5, label='Observed data')\n",
    "    plt.xticks([0, 1])\n",
    "    plt.legend(loc='best', fontsize=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3 - Challenger Space Shuttle Disaster\n",
    "\n",
    "Let's revisit this example from the MCMC lecture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temp (F), O-Ring failure?\n",
      "[[66.  0.]\n",
      " [70.  1.]\n",
      " [69.  0.]\n",
      " [68.  0.]\n",
      " [67.  0.]\n",
      " [72.  0.]\n",
      " [73.  0.]\n",
      " [70.  0.]\n",
      " [57.  1.]\n",
      " [63.  1.]\n",
      " [70.  1.]\n",
      " [78.  0.]\n",
      " [67.  0.]\n",
      " [53.  1.]\n",
      " [67.  0.]\n",
      " [75.  0.]\n",
      " [70.  0.]\n",
      " [81.  0.]\n",
      " [76.  0.]\n",
      " [79.  0.]\n",
      " [75.  1.]\n",
      " [76.  0.]\n",
      " [58.  1.]]\n"
     ]
    }
   ],
   "source": [
    "# load data \n",
    "challenger_data = np.genfromtxt(\"challenger_data.csv\", skip_header=1,\n",
    "                                usecols=[1, 2], missing_values=\"NA\",\n",
    "                                delimiter=\",\")\n",
    "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n",
    "print(\"Temp (F), O-Ring failure?\")\n",
    "print(challenger_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot it, as a function of temperature (the first column)\n",
    "plt.figure(figsize=(12, 5))\n",
    "plt.plot(challenger_data[:, 0], challenger_data[:, 1], 'ro', \n",
    "         markersize=15)\n",
    "plt.ylabel(\"Damage Incident?\",fontsize=20)\n",
    "plt.xlabel(\"Outside temperature (Fahrenheit)\",fontsize=20)\n",
    "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\",\n",
    "          fontsize=20)\n",
    "plt.yticks([0, 1], fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probabilistic model \n",
    "\n",
    "The defect probability is modeled as a function of the outside temperature:\n",
    "$$\\sigma(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$.\n",
    "\n",
    "The goal is to infer the latent variables $\\alpha$ and $\\beta$. \n",
    "\n",
    "We set normal priors on the latent variables - $\\alpha = \\mathcal{N}(0, 10^2)$ and $\\beta = \\mathcal{N}(0, 10^2)$ and the likelihood model is giveb by $p(x_i | \\alpha, \\beta, t) = \\mathrm{Bern}(x_i | \\sigma(t; \\alpha, \\beta) )$.\n",
    "\n",
    "The graphical model for this problem is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.43.0 (0)\n",
       " -->\n",
       "<!-- Title: space_shuttle_disaster Pages: 1 -->\n",
       "<svg width=\"134pt\" height=\"226pt\"\n",
       " viewBox=\"0.00 0.00 134.00 226.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 222)\">\n",
       "<title>space_shuttle_disaster</title>\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-222 130,-222 130,4 -4,4\"/>\n",
       "<g id=\"clust1\" class=\"cluster\">\n",
       "<title>cluster_0</title>\n",
       "<polygon fill=\"none\" stroke=\"blue\" points=\"28,-8 28,-154 98,-154 98,-8 28,-8\"/>\n",
       "<text text-anchor=\"middle\" x=\"63\" y=\"-14.8\" font-family=\"Times,serif\" font-size=\"14.00\">i=1,2...</text>\n",
       "</g>\n",
       "<!-- alpha -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>alpha</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-200\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"22.72\" y=\"-195.8\" font-family=\"Times,serif\" font-size=\"14.00\">α</text>\n",
       "</g>\n",
       "<!-- pi -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>pi</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"63\" cy=\"-128\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"57.56\" y=\"-124.8\" font-family=\"Times,serif\" font-size=\"14.00\">p</text>\n",
       "<text text-anchor=\"start\" x=\"64.56\" y=\"-124.8\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\">i</text>\n",
       "</g>\n",
       "<!-- alpha&#45;&gt;pi -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>alpha&#45;&gt;pi</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M35.35,-182.76C39.71,-174.28 45.15,-163.71 50.04,-154.2\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"53.23,-155.64 54.7,-145.15 47.01,-152.44 53.23,-155.64\"/>\n",
       "</g>\n",
       "<!-- beta -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>beta</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-200\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"95.11\" y=\"-195.8\" font-family=\"Times,serif\" font-size=\"14.00\">β</text>\n",
       "</g>\n",
       "<!-- beta&#45;&gt;pi -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>beta&#45;&gt;pi</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M90.65,-182.76C86.29,-174.28 80.85,-163.71 75.96,-154.2\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"78.99,-152.44 71.3,-145.15 72.77,-155.64 78.99,-152.44\"/>\n",
       "</g>\n",
       "<!-- xi -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>xi</title>\n",
       "<ellipse fill=\"lightgrey\" stroke=\"black\" cx=\"63\" cy=\"-56\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"57.56\" y=\"-52.8\" font-family=\"Times,serif\" font-size=\"14.00\">x</text>\n",
       "<text text-anchor=\"start\" x=\"64.56\" y=\"-52.8\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\">i</text>\n",
       "</g>\n",
       "<!-- pi&#45;&gt;xi -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>pi&#45;&gt;xi</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M63,-109.7C63,-101.98 63,-92.71 63,-84.11\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"66.5,-84.1 63,-74.1 59.5,-84.1 66.5,-84.1\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1468be208>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gcp = Digraph('space_shuttle_disaster')\n",
    "\n",
    "# setup the nodes \n",
    "gcp.node('alpha', label='<&alpha;>')\n",
    "gcp.node('beta', label='<&beta;>')\n",
    "with gcp.subgraph(name='cluster_0') as sg:\n",
    "    sg.node('pi', label='<p<sub>i</sub>>')\n",
    "    sg.node('xi', label='<x<sub>i</sub>>', style='filled')\n",
    "    sg.attr(color='blue')\n",
    "    sg.attr(label='i=1,2...')\n",
    "    sg.attr(labelloc='b')\n",
    "\n",
    "# setup the edges \n",
    "gcp.edge('alpha', 'pi')\n",
    "gcp.edge('beta', 'pi')\n",
    "gcp.edge('pi', 'xi')\n",
    "gcp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  `PyMC3` model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Challenger space shuttle disaster model:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\n",
       "            \\begin{array}{rcl}\n",
       "            \\text{alpha} &\\sim & \\text{Normal}(\\mathit{mu}=0.0,~\\mathit{sigma}=10.0)\\\\\\text{beta} &\\sim & \\text{Normal}(\\mathit{mu}=0.0,~\\mathit{sigma}=10.0)\\\\\\text{p} &\\sim & \\text{Deterministic}(\\text{Constant},~\\text{Constant},~\\text{alpha},~\\text{beta},~\\text{Constant})\\\\\\text{x} &\\sim & \\text{Bernoulli}(\\mathit{p}=\\text{p})\n",
       "            \\end{array}\n",
       "            $$"
      ],
      "text/plain": [
       "<pymc3.model.Model at 0x1468beba8>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# gather the data and apply preprocessing if any \n",
    "temp = challenger_data[:, 0]\n",
    "temp_scaled = (temp - np.mean(temp))/np.std(temp)\n",
    "data = challenger_data[:, 1]\n",
    "\n",
    "# instantiate the pymc3 model\n",
    "challenger_model = pm.Model()\n",
    "\n",
    "# define the graph \n",
    "with challenger_model:\n",
    "    # define the prior\n",
    "    alpha = pm.Normal('alpha', mu=0., sigma=10.)\n",
    "    beta = pm.Normal('beta', mu=0., sigma=10.)\n",
    "    \n",
    "    # get the probabilities of failure at each observed temp \n",
    "    p = pm.Deterministic('p', 1./(1. + tt.exp(alpha + beta*temp_scaled)))\n",
    "    \n",
    "    # define the likelihood \n",
    "    x = pm.Bernoulli('x', p=p, observed=data)\n",
    "print(\"Challenger space shuttle disaster model:\")\n",
    "challenger_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inference and posterior visualization\n",
    "\n",
    "Now let's infer the hidden parameters with VI. We will use both mean-field (i.e. diagonal covariance Gaussian) ADVI and full-rank (i.e. full rank covariance matrix Gaussian) ADVI. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 15.671: 100%|██████████| 20000/20000 [00:15<00:00, 1327.99it/s]\n",
      "Finished [100%]: Average Loss = 15.672\n"
     ]
    }
   ],
   "source": [
    "num_iter = 20000\n",
    "num_samples = 20\n",
    "with challenger_model:\n",
    "    method_1 = pm.ADVI()  # <- This method makes q a diagonal Gaussian\n",
    "    vi_approx_1 = pm.fit(n=num_iter, \n",
    "                       method=method_1,\n",
    "                       progressbar=True, \n",
    "                       obj_n_mc=num_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/20000 [00:00<?, ?it/s]/Users/rohitkt10/anaconda3/lib/python3.6/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "/Users/rohitkt10/anaconda3/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/Users/rohitkt10/anaconda3/lib/python3.6/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "Average Loss = 15.631: 100%|██████████| 20000/20000 [00:19<00:00, 1017.13it/s]\n",
      "Finished [100%]: Average Loss = 15.63\n"
     ]
    }
   ],
   "source": [
    "with challenger_model:\n",
    "    method_2 = pm.FullRankADVI()  # <- This method makes q a diagonal Gaussian\n",
    "    vi_approx_2 = pm.fit(n=num_iter, \n",
    "                       method=method_2,\n",
    "                       progressbar=True, \n",
    "                       obj_n_mc=num_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make sure that the ELBO has converged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 15))\n",
    "\n",
    "# ADVI\n",
    "plt.subplot(211)\n",
    "plt.plot(np.arange(num_iter), -vi_approx_1.hist)\n",
    "plt.ylabel('ELBO', fontsize=15)\n",
    "plt.xlabel('Iteration', fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.title('ADVI', fontsize=15);\n",
    "\n",
    "# Full rank ADVI\n",
    "plt.subplot(212)\n",
    "plt.plot(np.arange(num_iter), -vi_approx_2.hist)\n",
    "plt.ylabel('ELBO', fontsize=15)\n",
    "plt.xlabel('Iteration', fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.title('Full-rank ADVI', fontsize=15)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that both methods have converged to a local minimum.\n",
    "\n",
    "Let's get the variational posteriors $q$ for each case and compare."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the variational parameters and compute the post. pdf over a grid for ADVI\n",
    "mu, sigma = vi_approx_1.mean.eval(), vi_approx_1.std.eval()\n",
    "qtheta = pm.MvNormal.dist(mu=mu, cov=np.diag(sigma), shape=2)\n",
    "x1max, x2max = mu + 3.*sigma\n",
    "x1min, x2min = mu - 3.*sigma\n",
    "x1 = np.linspace(x1min, x1max, 50)\n",
    "x2 = np.linspace(x2min, x2max, 50)\n",
    "names = [g.name for g in vi_approx_1.groups[0].group]\n",
    "X1, X2 = np.meshgrid(x1, x2)\n",
    "Xgrid = np.vstack([X1.flatten(), X2.flatten()]).T\n",
    "advipdf = np.exp(qtheta.logp(tt.as_tensor(Xgrid)).eval()).reshape((50, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rohitkt10/anaconda3/lib/python3.6/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n"
     ]
    }
   ],
   "source": [
    "# get the variational parameters and compute the post. pdf over a grid for full rank ADVI\n",
    "mu, cov = vi_approx_2.mean.eval(), vi_approx_2.cov.eval()\n",
    "sigma = np.sqrt(np.diag(cov))\n",
    "qtheta = pm.MvNormal.dist(mu=mu, cov=cov, shape=2)\n",
    "\n",
    "x1max, x2max = mu + 3.*sigma\n",
    "x1min, x2min = mu - 3.*sigma\n",
    "x1 = np.linspace(x1min, x1max, 50)\n",
    "x2 = np.linspace(x2min, x2max, 50)\n",
    "names = [g.name for g in vi_approx_2.groups[0].group]\n",
    "X1, X2 = np.meshgrid(x1, x2)\n",
    "Xgrid = np.vstack([X1.flatten(), X2.flatten()]).T\n",
    "advifullrankpdf = np.exp(qtheta.logp(tt.as_tensor(Xgrid)).eval()).reshape((50, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 6))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.contourf(X1, X2, advipdf, 50)\n",
    "plt.xlabel('$\\\\'+names[0]+'$', fontsize=15)\n",
    "plt.ylabel('$\\\\'+names[1]+'$', fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.title('Joint Posterior over $(\\\\alpha, \\\\beta)$ - diagonal Gaussian posterior.', fontsize=15)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.contourf(X1, X2, advifullrankpdf, 50)\n",
    "plt.xlabel('$\\\\'+names[0]+'$', fontsize=15)\n",
    "plt.ylabel('$\\\\'+names[1]+'$', fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.title('Joint Posterior over $(\\\\alpha, \\\\beta)$ - full rank covariance.', fontsize=15)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how the simple diagonal Gaussian does not capture correlation between $\\alpha$ and $\\beta$,something we are able to recover with the full rank ADVI."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Posterior predictive distribution\n",
    "\n",
    "Here we will use a trace generated from the full rank Gaussian posterior to make posterior predictions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rohitkt10/anaconda3/lib/python3.6/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "/Users/rohitkt10/anaconda3/lib/python3.6/site-packages/pymc3/sampling.py:1247: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample\n",
      "  \"samples parameter is smaller than nchains times ndraws, some draws \"\n",
      "100%|██████████| 2000/2000 [00:00<00:00, 4036.76it/s]\n"
     ]
    }
   ],
   "source": [
    "trace = vi_approx_2.sample(10000)\n",
    "\n",
    "with challenger_model:\n",
    "    ppsamples = pm.sample_posterior_predictive(trace=trace, \n",
    "                                               samples=2000,\n",
    "                                               var_names=['p'])['p']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get posterior predictive mean and 95% interval\n",
    "ppmean = ppsamples.mean(axis=0)\n",
    "pp_lower, pp_upper = np.percentile(ppsamples, axis=0, q=[2.5, 97.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 8))\n",
    "plt.plot(temp, data, 'ro', markersize=12, label='Observed data')\n",
    "idx=np.argsort(temp)\n",
    "plt.plot(temp[idx], ppmean[idx], linestyle='--', linewidth=2.5, \n",
    "         label='Post. pred. mean prob.')\n",
    "plt.fill_between(temp[idx], pp_lower[idx], pp_upper[idx], \n",
    "                color='purple', alpha=0.25, label='95% Confidence')\n",
    "plt.ylabel(\"Probability estimate\",fontsize=20)\n",
    "plt.xlabel(\"Outside temperature (Fahrenheit)\",fontsize=20)\n",
    "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\",\n",
    "          fontsize=20)\n",
    "plt.yticks(np.arange(0., 1.01, 0.2), fontsize=20)\n",
    "plt.xticks(fontsize=20)\n",
    "plt.legend(loc='best', fontsize=20)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
